Various approaches to comparing subsets are discussed. Two approaches to direct single cluster clustering are described: seriation and moving center separation, which are reinterpreted as locally optimal algorithms for particular (mainly approximational) criteria. A moving center algorithm is based on a novel concept of reference point: the cluster size depends on its distance from the reference point. Five single cluster structures are considered in detail: Principal cluster as related to both seriation and moving center; Ideal fuzzy type cluster as modeling “ideal type” concept; Additive cluster as related to the average link seriation; Star cluster as a kind of cluster in a “non-geometrical” environment; Box cluster as a pair of interconnected subsets. Approximation framework is shown quite convenient in both extending the algorithms to multi cluster clustering (overlapping permitted) and interpreting.